NOC:Computational Number Theory and Algebra (USB)

Media Storage Type : 32 GB USB Stick

NPTEL Subject Matter Expert : Prof. Nitin Saxena

NPTEL Co-ordinating Institute : IIT Kanpur

NPTEL Lecture Count : 27

NPTEL Course Size : 14 GB

NPTEL PDF Text Transcription : Available and Included

NPTEL Subtitle Transcription : Available and Included (SRT)

Lecture Titles:

Lecture 1 - Introduction: Computation and Algebra
Lecture 2 - Background
Lecture 3 - GCD algorithm and Chinese Remainder Theorem
Lecture 4 - Fast polynomial multiplication
Lecture 5 - Fast polynomial multiplication (Continued...)
Lecture 6 - Fast integer multiplication and division
Lecture 7 - Fast integer arithmetic and matrix multiplication
Lecture 8 - Matrix Multiplication Tensor
Lecture 9 - Polynomial factoring over finite fields: Irreducibility testing
Lecture 10 - Equi-degree factorization and idea of Berlekamp's algorithm
Lecture 11 - Berlekamp's algorithm as a reduction method
Lecture 12 - Factoring over finite fields: Cantor-Zassenhaus algorithm
Lecture 13 - Reed Solomon Error Correcting Codes
Lecture 14 - List Decoding
Lecture 15 - Bivariate Factorization - Hensel Lifting
Lecture 16 - Bivariate polynomial factoring (Continued...)
Lecture 17 - Multivariate Polynomial Factorization
Lecture 18 - Multivariate Factoring - Hilbert's Irreducibility Theorem
Lecture 19 - Multivariate factoring (Continued...)
Lecture 20 - Analysis of LLL algorithm
Lecture 21 - Analysis of LLL algorithm (Continued...)
Lecture 22 - Analysis of LLL-reduced basis algorithm and Introduction to NTRU cryptosystem
Lecture 23 - NTRU cryptosystem (Continued...) and Introduction to Primality testing
Lecture 24 - Randomized Primality testing: Solovay-Strassen and Miller-Rabin tests
Lecture 25 - Deterministic primality test (AKS) and RSA cryptosystem
Lecture 26 - Integer factoring: Smooth numbers and Pollard's rho method
Lecture 27 - Pollard's p-1, Fermat, Morrison-Brillhart, Quadratic and Number field sieve methods